Elastography is a promising new imaging technique that provides diagnostic information not available with conventional ultrasonography. The image formation process can be complex; in particular, the appearance of the elastogram and the accuracy and precision of the strain measurement strongly depend on the many data acquisition and signal processing parameters. The objective of this project is to provide objective criteria for assessing the quality of elastograms with respect to sonograms to guide development of the modality for diagnosis and to optimize diagnostic performance for specific imaging tasks. This project focuses on the statistical properties of elastography, with the specific aim of measuring the low-contrast detectability of circular targets under noise-limited conditions. Analysis of the strain estimation method provides the probability models that accurately represent elastographic image data. From the probability models, likelihood ratios are derived to discover the strategy of the ideal observer for target detection and to measure the corresponding signal-to-noise ratio (SNR). Observer performance measurements are planned to measure the SNR for expert human observers. From the SNR measurements we compute visual detection efficiencies for elastography. Detection efficiency is the evaluation criterion we propose for optimizing signal processing methods, assessing the accuracy of assumptions regarding how tissues respond to an applied stress, and comparing low-contrast detectability with that of sonography. Project 3 offers a means for evaluating the tissue motion models developed in Project 1 and the signal processing methods developed in Project 2. The statistical analysis of elastographic images and the SNR analysis aspects of the project stand alone.